Mathematics: The ratio of carbon-14 to carbon-12 in a piece of wood discovered in a cave is r = 1/816. estimate the age of the piece of wood.

The ratio of carbon-14 to carbon-12 in a piece - id1412371718, DarcieMATHlin6217

Arealbot

11.03.2022

Age of the piece of wood was found out to be 55,434.65 years

Step-by-step explanation:

The ratio of carbon-14 to carbon-12 in a piece of wood discovered in a cave is

$=\dfrac{1}{816}$

i.e $\dfrac{N}{N_0}=\dfrac{1}{816}$

We know that,

$t=\dfrac{\ln \frac{N}{N_0}}{-0.693}\cdot t_{\frac{1}{2}}$

Where $t_{\frac{1}{2}}$ is the half-life of the isotope carbon 14, which is 5730 years.

Putting the values,

$t=\dfrac{\ln \dfrac{1}{816}}{-0.693}\cdot 5730$

$=\dfrac{-6.7044}{-0.693}\cdot 5730$

$=\dfrac{6.7044\times 5730}{0.693}$

=55,434.65 years

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npaslayoy1bzj

25.08.2022

line up the dot with the numbers that are in the same line X is always frist and the Y

A= (-4,5)

B=(3,-3)

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